ELEMENTS OF RARE EARTH MAGNETISM - Rare Earth Magnetism: Structures and Excitations - page 34

Fig. 1.12. Characteristic band energies for the trivalent lanthanides,
for a common value of the atomic radius S , after Skriver (1983). The
values of the potential v(S) and the exchange-correlation energy ε xc at
the atomic sphere are shown, together with the bottom, B l ,thecentre,
C l ,andthetop, A l ,ofthe6 s ,6 p ,and5 d bands, and the Fermi level
ε F . The relative lowering of the 6 s band with increasing atomic number
reduces the 5 d occupancy, which in turn changes the crystal structure.
see, for the crystal structure. The reason for the fall in the band en-
ergies is the increase of the nuclear charge with atomic number, which
is incompletely screened by the additional f electrons. The potential
v eff ( r ) in (1.2.12) is therefore on average increasingly negative, and in
order to maintain an unchanged boundary condition, as expressed by
the logarithmic derivative, the band energies must decrease accordingly.